Results 1 to 10 of about 947,467 (42)

Pell Numbers with Lehmer property [PDF]

arXiv, 2015
In this paper, we prove that there is no number with the Lehmer property in the sequence of Pell numbers.
arxiv  

Convolution identities for Tetranacci numbers [PDF]

arXiv, 2016
We give convolution identities without binomial coefficients for Tetranacci numbers and convolution identities with binomial coefficients for Tetranacci and Tetranacci-type numbers.
arxiv  

Smooth affine group schemes over the dual numbers [PDF]

Épijournal de Géométrie Algébrique, 2019
We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 \to \text{Lie}(G, I) \to E \to G \to 1$ where G is an affine, smooth group ...
Matthieu ROMAGNY, Dajano Tossici
doaj   +1 more source

Periodic balanced binary triangles [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$.
Jonathan Chappelon
doaj   +1 more source

Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms [PDF]

, 2003
In a letter to Tate (published in Israel J. Math. in 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space constructed ...
Ghitza, Alexandru
core   +2 more sources

Well-poised generation of Ap\'ery-like recursions [PDF]

, 2003
The idea to use classical hypergeometric series and, in particular, well-poised hypergeometric series in diophantine problems of the values of the polylogarithms has led to several novelties in number theory and neighbouring areas of mathematics. Here we
Apéry, Beukers, Beukers, Beukers, Beukers, Gutnik, Gutnik, Nesterenko, Petkovšek, Rivoal, Wadim Zudilin, Zudilin, Zudilin, Zudilin   +13 more
core   +2 more sources

Hyperelliptic curves, continued fractions, and Somos sequences [PDF]

, 2006
We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion.
van der Poorten, Alfred J.
core   +3 more sources

Congruences concerning Jacobi polynomials and Ap\'ery-like formulae [PDF]

, 2012
Let $p>5$ be a prime. We prove congruences modulo $p^{3-d}$ for sums of the general form $\sum_{k=0}^{(p-3)/2}\binom{2k}{k}t^k/(2k+1)^{d+1}$ and $\sum_{k=1}^{(p-1)/2}\binom{2k}{k}t^k/k^d$ with $d=0,1$. We also consider the special case $t=(-1)^{d}/16$ of
Apèry R., Borwein J. M., Hessami Pilehrood Kh., KH. HESSAMI PILEHROOD, Koecher M., R. TAURASO, Szegö G., T. HESSAMI PILEHROOD   +7 more
core   +1 more source

Characteristic ideals and Selmer groups [PDF]

, 2014
Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally ramified, we define
Bandini, Andrea, Bars, Francesc, Longhi, Ignazio   +2 more
core   +4 more sources

Twisted character of a small representation of GL(4)

, 2006
We compute by a purely local method the (elliptic) twisted by transpose-inverse character \chi_{\pi_Y} of the representation \pi_Y=I_{(3,1)}(1_3x\chi_Y) of G=GL(4,F), where F is a p-adic field, p not 2, and Y is an unramified quadratic extension of F ...
Flicker, Yuval Z., Zinoviev, Dmitrii
core   +1 more source